Question

One cubic meter of nitrogen at 40°C and 340kPa is compressed isoentropically to 0.2m^3. Calculate the final pressure when the nitrogen is reduced to that volume. What is the modulus of elasticity at the beginning and end of the compression? (k = 1.4)

Answer 1

Answer:

a)P₂=3236.21 KPa

b)E=3620.26 KPa

Explanation:

Given that

V₁= 1 m³

T₁=40°C

P₁= 340 KPa

V₂=0.2 m³

k= 1.4

We know that for  isentropic process

$PV^{k}=C$

$P_1V_1^{k}=P_2V_2^{k}$

$340\times 1^{1.4}=P_2\times 0.2^{1.4}$

P₂=3236.21 KPa

Final pressure of gas P₂=3236.21 KPa

We know that modulus of elasticity

$E=\dfrac{dP}{-\dfrac{dV}{V}}$

$E=\dfrac{3236.21-340}{-\dfrac{0.2-1}{1}}$

E=3620.26 KPa